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On generalized Hamming weights of BCH codes
IEEE Transactions on Information Theory, 1994A method is introduced to determine the generalized Hamming weights [\textit{V. K. Wei}, IEEE Trans. Inf. Theory 37, No. 5, 1412--1418 (1991; Zbl 0735.94008)] of certain families of codes, by the use of a geometric description of their dual. This method is ruled out by the authors to calculate some generalized weights of BCH(2) and BCH(3).
van der Geer, G.B.M., van der Vlugt, M.
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Generalized Hamming weights of linear codes
IEEE Transactions on Information Theory, 1992Summary: The generalized Hamming weight, \(d_ r(C)\), of a binary linear code \(C\) is the size of the smallest support or any \(r\)-dimensional subcode of \(C\). The parameter \(d_ r(C)\) determines the code's performance on the wire-tap channel of Type II. We derive bounds on \(d_ r(C)\) and, in some cases exact expressions.
Tor Helleseth +2 more
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Generalized Hamming weights of trace codes
IEEE Transactions on Information Theory, 1994A general bound is given for the generalized Hamming weights [\textit{V. Wei}, same journal 37, No. 5, 1412-1418 (1991; Zbl 0735.94008)]\ of the trace code of geometric Goppa codes. Then, many examples are ruled out. For instance, the authors found, in the case of the dual of the \(t\)-error correcting BCH code of length \(n= p^m-1\): \[ d_r(\text{BCH}
Henning Stichtenoth, Conny Voss
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On the generalized Hamming weights of cyclic codes
IEEE Transactions on Information Theory, 1997Summary: We prove several results on the generalized Hamming weights (GHW's) of linear codes, particularly for cyclic codes. Based on these and previously known results, we give some efficient algorithms for computing GHW hierarchy of cyclic codes. We give complete weight hierarchy for each of the binary cyclic codes of odd lengths \(\leq 31\). A table
Heeralal Janwa, Arbind K. Lal
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Classifier Systems with Hamming Weights
1988Classifier systems are learning systems that use a genetic algorithm to carry out their learning. With the exception of work by Lashon Booker, researchers in the field have employed exact matching procedures when using classifier systems. In this paper we describe three learning problems that create difficulties for classifier systems using exact ...
Lawrence Davis, David K. Young
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2005
Let R and B be two sets of n points. A ham-sandwich cut is a line that simultaneously bisects R and B, and is known to always exist. This notion can be generalized to the case where each point p ∈ R ∪ B is associated with a weight wp. A ham-sandwich cut can still be proved to exist, even if weights are allowed to be negative.
Prosenjit Bose, Stefan Langerman
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Let R and B be two sets of n points. A ham-sandwich cut is a line that simultaneously bisects R and B, and is known to always exist. This notion can be generalized to the case where each point p ∈ R ∪ B is associated with a weight wp. A ham-sandwich cut can still be proved to exist, even if weights are allowed to be negative.
Prosenjit Bose, Stefan Langerman
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On the Weight of Halfspaces over Hamming Balls
SIAM Journal on Discrete Mathematics, 2014For $S \subseteq \{0,1\}^n$, a Boolean function $f: S \to \{-1,1\}$ is a halfspace over $S$ if there exist $w \in \mathbb{R}^n$ and $\theta \in \mathbb{R}$ such that $f(x)=\mathrm{sign}(w \cdot x - \theta)$ for all $x \in S$. We give bounds on the size of integer weights $w_1,\dots,w_n \in \mathbb{Z}$ that are required to represent halfspaces over ...
Philip M. Long, Rocco A. Servedio
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Weighted Gaussian Loss based Hamming Hashing
Proceedings of the 29th ACM International Conference on Multimedia, 2021Recently, deep Hamming hashing methods have been proposed for Hamming space retrieval which enables constant-time search by hash table lookups instead of linear scan. When carrying out Hamming space retrieval, for each query datapoint, there is a Hamming ball centered on the query datapoint, and only the datapoints within the Hamming ball are returned ...
Rong-Cheng Tu +6 more
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Weight Functions and Generalized Hamming Weights of Linear Codes
Problems of Information Transmission, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the generalized Hamming weights of product codes
IEEE Transactions on Information Theory, 1993Summary: The \(r\)th generalized Hamming weight of a linear code is the minimum support size of any \(r\)-dimensional subcode. It has been found useful in the studies of cryptography and trellis coding. We derive several results on expressing the generalized Hamming weights of a product code in terms of those of its component codes. We also formulate a
WEI, VK, YANG, KC
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